Advances in Risk Management

78 MANAGING INTEREST RATE RISK UNDER NON-PARALLEL CHANGES

Table 4.3Relative behavior of the bonds included in the portfolio 1 with
respect to a parallel change in the yield curve

Yield Bond A Bond B Bond C
Change
Accumulated Yield Accumulated Yield Accumulated Yield
value (%) value (%) value (%)

5 85.176 −29.646 75.759 −48.480 77.809 −44.381

4.5 86.757 −26.485 78.042 −43.915 79.966 −40.067

4 88.374 −23.250 80.444 −39.110 82.242 −35.514

3.5 90.029 −19.940 82.974 −34.051 84.648 −30.703

3 91.722 −16.554 85.638 −28.722 87.191 −25.616

2.5 93.455 −13.088 88.447 −23.105 89.883 −20.233

2 95.229 −9.541 91.409 −17.181 92.735 −14.529

1.5 97.044 −5.911 94.534 −10.931 95.758 −8.482

1 98.901 −2.196 97.833 −4.333 98.967 −2.064

0.5 100.803 1.606 101.317 2.635 102.376 4.752

0 102.75 5.5 105 10 106 12

−0.5 104.742 9.485 108.892 17.785 109.856 19.713

− 1 106.782 13.565 113.010 26.021 113.964 27.928

−1.5 108.871 17.743 117.369 34.738 118.343 36.687

− 2 111.010 22.020 121.983 43.967 123.017 46.034

−2.5 113.200 26.401 126.872 53.744 128.008 56.016

− 3 115.443 30.887 132.053 64.107 133.344 66.688

−3.5 117.740 35.481 137.547 75.095 139.054 78.108

− 4 120.093 40.186 143.376 86.753 145.168 90.337

−4.5 122.502 45.005 149.563 99.127 151.723 103.447

− 5 124.971 49.942 156.133 112.267 158.756 117.512

Table 4.4 includes the results for both portfolios. The accumulated value
of portfolio 1 is the weighted average of those of its bonds. As in Table 4.3,
the first column shows the changed size in the yield curve. The last column
shows the difference between both yields. Anegative (positive) value means
that portfolio 1 generates a higher (lower) yield than portfolio 2.
The strategy to follow with these portfolios depends on the sign of the
shift in the yield curve. As the last column of this table shows, portfolio 1
outperforms portfolio 2 if interest rates increase. On the other hand, we can
see that portfolio 2 provides a greater yield than portfolio 1 when interest
rates fall.
This result arises because the generalized duration with respect to the
short-term interest rate of portfolio 1 is lower than that of portfolio 2. Hence,